AbstractIn this paper, we review problems associated with sparse matrices. We formulate several theorems on the allocation of a quasi-block '/> Decomposition in Multidimensional Boolean-Optimization Problems with Sparse Matrices
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Decomposition in Multidimensional Boolean-Optimization Problems with Sparse Matrices

机译：稀疏矩阵的多维布尔优化问题中的分解

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AbstractIn this paper, we review problems associated with sparse matrices. We formulate several theorems on the allocation of a quasi-block structure in a sparse matrix, as well as on the relation of the degree of the quasi-block structure and the number of its blocks, depending on the dimension of the matrix and the number of nonzero elements in it. Algorithms for the solution of integer optimization problems with sparse matrices that have the quasi-block structure are considered. Algorithms for allocating the quasi-block structures are presented. We describe the local elimination algorithm, which is efficient for problems with matrices that have a quasi-block structure. We study the problem of an optimal sequence for the elimination of variables in the local elimination algorithm. For this purpose, we formulate a series of notions and prove the properties of graph structures corresponding to the order of the solution of subproblems. Different orders of the elimination of variables are tested.
机译： Abstract 在本文中，我们回顾了与稀疏矩阵相关的问题。我们根据稀疏矩阵中准块结构的分配以及准块结构的程度与其块数之间的关系，制定了几个定理，具体取决于矩阵的维数和数目其中的非零元素。考虑具有稀疏矩阵且具有准块结构的整数优化问题的求解算法。提出了分配准块结构的算法。我们描述了局部消除算法，该算法对于具有准块结构的矩阵问题非常有效。我们研究了在局部消除算法中消除变量的最佳顺序问题。为此，我们提出了一系列概念，并证明了与子问题解的顺序相对应的图结构的性质。测试了消除变量的不同顺序。

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